Problem 70E

The table gives the US population from 1790 to 1860. Year Population 1790 3, 929, 000 1800 5, 308, 000 1810 7, 240, 000 1820 9, 639, 000 1830 12, 861, 000 1840 17, 063, 000 1850 23, 192, 000 1860 31, 443, 000 a Use a graphing calculator or computer to fit an exponential function to the data. Graph the data points and the exponential model. How good is the fit? b Estimate the rates of population growth in 1800 and 1850 by averaging slopes of secant lines. c Use the exponential model in part a to estimate the rates of growth in 1800 and 1850. Compare these estimates with the ones in part b. d Use the exponential model to predict the population in 1870. Compare with the actual population of 38, 558, 000. Can you explain the discrepancy?

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